NEW YORK — The New York Rangers are likely more relieved than ecstatic now that they have outlasted the pesky Ottawa Senators.

It wasn’t easy, and after a home loss in Game 5, it almost wasn’t likely. But the Eastern Conference’s top-seeded team gutted out a big road win and then made it count Thursday night when the Rangers held off the Senators 2-1 in Game 7 to advance to the second round.

“You don’t want to relax too much,” said forward Derek Stepan, who had three points in the Rangers’ Game 6 win and then helped set up the opening goal in the clincher. “We have a big round ahead of us, and we have to make sure we stay focused and keep that emotion high.”

Defensemen Marc Staal and Dan Girardi scored 4:18 apart in the second period, Henrik Lundqvist made 26 saves and the Rangers eliminated the eighth-seeded Senators — completing a rally from a 3-2 hole after losing Game 5.

“We were talking about it in Ottawa that if we could bring it back here, the fans would be behind us,” Girardi said. “The way we play all year got us ready for games like this. We came with a great effort (in Ottawa) and another one tonight.”

Staal broke the scoreless deadlock, and Girardi gave the Rangers a 2-0 lead with his first career NHL playoff goal. Lundqvist allowed Daniel Alfredsson’s power-play goal in the second but stood tall the rest of the way to send the Rangers into a second-round matchup with the seventh-seeded Washington Capitals.

The Rangers hadn’t hosted a Game 7 since their Stanley Cup victory over the Vancouver Canucks in 1994, but they stayed perfect at home in deciding games — winning their fourth. New York is 4-5 overall in Game 7, and the Senators fell to 0-5.

“We knew they were going to come out strong,” said Senators goalie Craig Anderson, who made 27 saves. “I just wanted to make sure that I gave my team an opportunity to win the hockey game — make the next save for the guys.”

Lundqvist withstood tons of pressure from the Senators, who spent most of the closing five minutes in the Rangers’ end. The win wasn’t secure until Sergei Gonchar tripped Carl Hagelin as he skated toward the empty net with 36.2 seconds left.

“It was a hard series against a very good team,” Rangers coach John Tortorella said. “I thought both teams went toe to toe in all areas of the game. Sometimes the first round is the hardest round. That’s all this is, one round.”

KANSAS CITY, Mo. — Tyreek Hill didn’t know what to do when he started hearing thousands of people in Arrowhead Stadium chanting his name, even as he stood all alone on the frozen turf waiting for the punt.